Rabah-IPEC-Sapporo2010

8/6/2019 Rabah-IPEC-Sapporo2010

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Direct Torque Control Scheme

For Dual-Three-Phase Induction Motor

R. Zaimeddine, T. UndelandDepartment of Electric Power EngineeringEnergy Conversion Research Group

Norwegian University of Science and Technology

O.S. Bragstad plass 2E, 7491, Trondheim, Norway

Abstract - In this paper, Direct Torque Control (DTC)

algorithms for dual three-phase induction motor fed by six

phases Voltage Source Inverter (VSI) is described. The

induction machine has two sets of three-phase stator

windings spatially shifted by arbitrary angle. The machine

dynamic model is based on the vector space decomposition

theory. Optimal switching strategies to control the machine

for different winding shift angles are proposed, the selection

is based on the value of the stator flux and the torquewithout need for any mechanical sensor. Then, the amplitude

and the rotating velocity of the flux vector can be controlled

freely. Both approaches are simulated for dual three-phase

induction motor (DTPIM). The results obtained show that

both fast torque and optimal switching logic can be obtained.

Key Words - Dual three-phase induction motor, Direct torque

control, Fast torque response, Sensorless vector control,

Voltage source inverter, Switching strategy optimisation.

I. INTRODUCTION

Multiphase Motor drives have been proposed for high

power applications, such as traction, electric/hybridvehicles, locomotive traction, aircraft applications and

ship propulsion, where some specific advantages can be

better exploited justifying the higher complexity

(increased number of the current sensors, gate drive

circuits, auxiliary circuitry, and large stator harmonic

currents which result increasing the cost of the drivesystem) compared to the three phase machine solution [1].

The main advantage of multiphase drives is the

splitting of the controlled power on more inverter legs,

reducing the single switch current stress compared with

the classical three-phase converters. In addition toenhancing power rating, it is also believed that drive

systems with such multiphase redundant structure willimprove the reliability at the system level [2].

One common example of such structure is the dual

three-phase induction machine fed by six-phase voltage

source inverter. The principle advantage of this structure

is the elimination of the sixth harmonic torque pulsation

encountered in VSI fed three-phase induction machines.

With the increasing of the stator winding number, there

are many ways to select voltage space vectors to improve

the drive performances. This paper describes a control

scheme for direct torque and flux control of inductionmachines fed by a six-phase voltage source inverter using

a switching table. In this method, the output voltage is

selected and applied sequentially to the machine through alook-up table so that the flux is kept constant and the

torque is controlled by the rotating speed of the stator

flux. The direct torque control (DTC) is one of the

actively researched control scheme which is based on thedecoupled control of flux and torque providing a very

quick and robust response with a simple control

construction in ac drives [3], [4].

In this paper, the authors propose a DTC scheme for

high power applications with optimal switching strategiesapplied for different DTPIM configurations.

II. MACHINE MODEL

To model the dual three-phase induction machine, the

vector space decomposition (VSD) approach has beenused under the following assumptions:

1. The machine windings are sinusoidal distributed and

the rotor cage is equivalent to a six-phase wound rotor.

2. Flux path is linear.

3. The magnetic saturation and the core loss are neglected.

4. The mutual leakage inductances are neglected.

The vector space decomposition theory (VSD) has been

introduced to transform the original six-dimensional space

of the machine into three two dimensional orthogonal

subspaces (, ), (1, 2) and (z1, z2), introducing a 6 x 6transformation matrix [T6].

[ ]

++

++

=

111000

000111

)3

5sin()

3sin()sin()

3

2sin()

3

4sin()0sin(

)3

5cos()

3cos()cos()

3

2cos()

3

4cos()0cos(

)3

4sin()

3

2sin()sin()

3

4sin()

3

2sin()0sin(

)3

4cos()

3

2cos()cos()

3

4cos()

3

2cos()0cos(

3

16

T

(1)

Where is the shift between the two sets of three-phase

windings.

The modeling and control of dual three-phase induction

machine can be greatly simplified with a propertransformation matrix which maps the description of a

vector with respect to the original six-dimensional frame

spanned by six standard base vectors to a new reference

frame. According to the VSD, the composition of the

vectors (, , 1, 2, z1, z2) introducing a 6 X 6

transformation matrix [T6] having the followingproperties, [1]:

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The 2010 International Power Electronics Conference

978-1-4244-5395-5/10/$26.00 2010 IEEE


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The fundamental components of the machine

variables and the harmonics of the orderk=12m 1, (m = 1, 2, 3) are mapped in the (,) subspace. These components will contribute to

the air-gap flux.

The harmonics of order k = 6m 1, (m = 1, 3, 5

) are mapped in the (1, 2) subspace. These

harmonics (the 5th

, 7th

, 17th

, 19th

) will notcontribute to the air-gap flux since the (, ) and

(1, 2) subspaces are orthogonal.

The zero sequence components of order k=3m(m=1, 2, 3) which are not related toelectromechanical energy conversion, are

mapped into the (z1, z2) subspace to form theconventional zero sequence components.

A. Machine model in (, ) subspace

By applying the rotating transformation matrix, the

following equation combines the stator and rotorequations in the stationary reference frame (-). Using

complex vector notation, the machine model is:

+=

+=

+=

+=

si

mL

ri

rL

r

ri

mL

si

sL

s

rrj

rp

ri

rr

sp

si

sr

sv

0(2)

+=

+=

+=

+=

+=

rj

rr

sj

ss

rji

ri

ri

sji

si

si

sjv

sv

sv

(3)

Where:

=

=

=

dt

dp

Pr .

L3=M

L3+L=L

L3+LL

ms

mrlrr

mslss

(4)

As shown by (2) and (3), the torque production

involves only quantities in the (, ) subspace, and

consequently the machine control is simplified since it

need to act only on a two dimensional subspace, [5].

Torque control of an induction motor can be achieved on

the basis of its model developed in a two axis (, )

reference frame stationary with the stator winding. In thisreference frame and with conventional notations, the

electrical mode is described by the following equations:

)ii(P ssssem = (5)

Where P is the pole pairs

The mechanical mode associated to the rotor motion is

described by:

)(=

Lemdt

dJ (6)

)(L and em are respectively the load torque and

the electromagnetic torque developed by the machine.

So; the equivalent circuit in the (, ) subspace is similarto the equivalent circuit of the standard three-phase

machine:

Fig.1. Single-phase equivalent circuit of the machine in the (, )

subspace.

B. Machine model in (1, 2) subspace

The machine model in the (1, 2) subspace describestwo independent passive RL Circuit as:

+

+

=

2

1.

.0

0.

2

1

si

si

pls

Ls

R

pls

Ls

R

sv

sv(7)

Fig.2. Single-phase equivalent circuit in the (1, 2) subspace.

C. Machine model in (z1, z2) subspace

+

+

=

2

1.

.0

0.

2

1

szi

szi

pls

Ls

R

pls

Ls

R

szv

szv

(8)

Fig.3. Single-phase equivalent circuit in the (z1-z2) subspace.

Vsz1, z2Isz1 ,z2vsz1z2 isz1z2

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3/8

From the modeling of DTPIM, it can be noted that:

The electromechanical energy conversion variables are

mapped in the (, ) subspace, while the non

electromechanical energy conversion variables can be

found in the other two subspaces.

The current components in the (1, 2) and (z1-z2)subspaces do not contribute to the air-gap flux and they

are limited only by the stator resistance and stator leakage

inductance. These currents will produce only losses and

consequently should be controlled to be as small as

possible.

The control of the dual- three phase induction machine

is greatly simplified, since it can be solved with the

equivalent circuit in (, ) subspace being similar to the

equivalent circuit of a three-phase machine.

III. THE SIX-PHASE VOLTAGE SOURCEINVERTER

The six-phase voltage source inverter (VSI) contains a

switching network of 12 power switches arranged to form

6 legs, each leg supplies one motor phase, Fig.4 . Only

one of the power switches of the same leg can operate in

the on state to avoid the shortcircuit of the dc-link,

where (Sa1,Sb1,Sc1,Sa2,Sb2,Sc2) are switching functions of

the inveter legs with value 1 indicate that the upperswithes in the corresponding switching arms are on,

while the 0 indicate the on state of the lower

switches.

So, 26

= 64 possible states can be obtained. In this

case, the voltages applied to the dual three-phaseinduction motor are determined only by the inverterswitching modes and regarded as discrete values.

Fig.4. Voltage source inverter fed dual three-phase induction motor

The machine phase voltage can be computed using theswitching function associated to one inverter leg; that is

defined as:

=

=

on)isswitch(loweroffisswitchuppertheif0,Sj

off)isswitch(loweronisswitchuppertheif1,Sj

where : j = a1,b1,c1,a2,b2,c2.

For the machine having isolated neutral points, the

machine phase voltages are separately computed for eachthree-phase set as:

==

=

==

=

2c,

2b,

2aj;

dc).V

1,

1,

1ak

.3

1-

j(S

jsV

1c,

1b,

1ai;

dc).V

1,

1,

1ak

.3

1-

i(S

isV

kS

cb

kS

cb

(9)

The principal schematic of six-phase voltage sourceinverter supplying the DTPIM is given by fig.4; where theswitches of the half superior bridge are noted Sa1, Sb1, Sc1for stator 1 and Sa2, Sb2, Sc2 for stator 2. Either n1 or n2 arethe neutrals of the stator 1 and stator 2 respectively, ando is the neutral point of the source.

Therefore, we deduce the matrix [C] that represents the

connection between VSI and DTPIM that gives the

boundary voltages of the machine as function of theoutput voltages of the inverter.

=

ocv

obv

oav

ocv

obv

oav

.

csv

bsv

asv

csv

bsv

asv

2

2

2

1

1

1

211000

121000

112000

000211

000121

000112

3

1

2

2

2

1

1

1

(10)

[Vs]=[C].[Vinv] (11)

[Vinv] = Vdc. [K] =Vdc. [ Sa1 Sb1 Sc1 Sa2 Sb2 Sc2 ]T

(12)

So : [Vs] = Vdc . [C] . [ Sa1 Sb1 Sc1 Sa2 Sb2 Sc2 ]T

(13)

Such that : [K] is the vector that gives the positions ofthe switches (S=0: Off, S=1: On).

A. Inverter voltage vectors on the new reference frame

Using the VSD transformation matrix [T6] and thematrix equation (10), the projection of the voltage

components of the machine in the (, ), (1, 2) and (z1,

z2) subspaces for (phase shift angle = /6) are computedas:

[Vst]= [Vs Vs Vs1 Vs2 Vsz1 Vsz2 ]T

= [T6] . [Vs] (14)

A combinatorial analysis of the inverter switch stateshows 64 switching modes (modes of commutations), in

other words 64 output voltage vectors can be applied tothe DTPIM.

111 cban

222 cban

1asv

2asv

1bsv

1asv

1asv

2csv

a1 a2 b1 c1b2 c2Vdc

2csi

1csi

2bsi

1bsi

2asi

1asi

3009



4/8

=

2

2

2

1

1

1

000000 000000

12

1

2

1

2

3

2

30

02

3

2

3

2

1

2

11

12

1

2

1

2

3

2

30

02

3

2

3

2

1

2

11

3

2

1

2

1

cSb

Sa

Sc

Sb

Sa

S

.dc

V

szvszv

sv

sv

svsv

(15)

Combining the relations written above (15), we get the

projection of the voltage vectors generated by inverter onthe planes (, ), (1, 2) and (z1, z2). According to thisequation, no voltage components are generated in the (z1,z2) subspace; for this reason, the machine topology withtwo separate neutral points is usually preferred.

Considering all switching states and using the

appropriate transformation matrix, the projections of thenormalized voltage vectors in the remaining orthogonal

subspaces (, ) and (1, 2) are done for the differentphase shift angles between the two stators for = 0, /6,/3 respectively; Where the decimal numbers in thefigures represent the inverter switching state N, i.e.; its binary equivalent number gives the values of the

switching function of the inverter legs considered in theorder [Sa1 Sb1 Sc1 Sa2 Sb2 Sc2 ], such that the vectors ofnumberNare obtained for different switch configurations

of the inverter.

For =30, the inverter provides 48 independent non-zero voltage vectors and 4 zero voltage vectors either in(, ) or (1, 2). The representation of the space voltage

vectors of the six-phase voltage source inverter for allswitching states forming the three-layer hexagon centeredat the origin of the plane and a zero voltage vector at theorigin of the plane. According to the magnitude of the

voltage vectors we divide them into five groups: the zerovoltage vectors (have 4 switching states), the smallvoltage vectors (12 switching states), the middle voltagevectors (24 switching states), the large voltage vectors (12switching states) and the largest voltage vectors (12switching states). Where the projections of the 12 largestvoltage vectors generated by the inverter in (, ), are the

smallest 12 voltage vectors in (1, 2) for the sameswitching modes.

For =0 and =60, using the appropriatetransformation matrix, the inverter provides 18independent non-zero voltage vectors and 10 zero voltagevectors either in (, ) or (1, 2). Where the

representation of the space voltage vectors of the six- phase voltage source inverter for all switching statesaccording to the magnitude of the voltage vectors are

divided into four groups: the zero voltage vectors (have10 switching states), the small voltage vectors (36switching states), the middle voltage vectors (12 switchingstates) and the large voltage vectors (6 switching states).Where the projection of the 6 largest voltage vectors

generated by the inverter in (, ) are the zero voltagevectors in (1, 2) for the same switching modes.

IV. PRINCIPLE OF THE DIRECT TORQUE CONTROL

The industrial AC drives require high dynamicperformance over a wide range of speed. A controller witha fast torque response and decoupled control of the statorflux and electromagnetic torque without inner controlloops is required. In this area, the direct torque control

(DTC) approach was initiated by I.TAKAHASHI in themiddle of 1980s and enhanced by many authors; this new

technique is characterized by the simplicity, goodperformance, robustness and absence of PI regulators, [3].

The direct torque control of induction machine is based

on direct determination of the commutation sequences ofthe inverter switches; it is possible to control directly thestator flux and torque by selecting an appropriateswitching inverter states. The DTC scheme requires the

estimation of the stator flux and torque which arecompared to their reference values and the resulting errorsare fed to the hysteresis controller of stator flux and

torque.

The purpose of the direct torque control of inductionmachine is to restrict the stator flux and torque errorswithin respective limits of the flux and torque hysteresisbands by an appropriate selection of the inverter switchingstates.

The switching table-direct torque control (ST-DTC)

basic scheme for dual-three-phase induction motor drivesis shown in fig.5. Based on the estimated stator fluxposition, hysteresis controllers for torque and flux are

used to generate the inverter switching functions throughan optimal switching table (ST). The key issue for ST-DTC is the ST design in other to get sinusoidal machinephase currents, by minimizing the current components in

the (1, 2) subspace.

Fig.5. Block diagram of direct torque control

The six-phase voltage source inverter provides moreoutput voltage vectors compared with three-phase one; in

other word the six-phase voltage source inverter provides64 possible states rather than 8 possible states of the three-

phase two level inverter.

DTPIM

D

T

C

Voltage

Estimator

[ ]6T

FluxEstimation

TorqueEstimation

vs

is

111 csbsasv

222 csbsasv

3

3

+ -Vdc

Vdc

s

s

+

+

-

-

s

111 cbaS

222 cbaS

111 csbsasi

222 csbsasi

s*

em*

em

3010



5/8

The 64 output voltage vectors of the six-phase voltage

source inverter are used to synthesize the voltage to theDTPIM in order to control the flux and the torque bydeveloping the switching table.

The stator flux evaluation can be carried out bydifferent techniques depending on whether the rotor

angular speed or (position) is measured or not. Forsensorless application, the voltage model is usuallyemployed [6]. The stator flux can be evaluated byintegrating from the stator voltage equation.

= dtsIsRVsts )()( (16)

This method is very simple requiring the knowledge ofthe stator resistance only. The effect of an error in Rs isusually neglected at high excitation frequency but

becomes more serious as the frequency approaches zero.The electromagnetic torque is estimated from the flux andcurrent information as:

)ii(P ssssem = (17)

The stator flux angle, s is calculated by:

s

ss

arctan= (18)

and quantified into 6 or 12 levels depending on which

sector the flux vector falls into. Different switchingstrategies can be employed to control the torque according

to whether the flux has to be reduced or increased.Each strategy affects the drive behavior in terms of

torque and current ripple, switching frequency and two orfour-quadrant operation capability.

Assuming the voltage drop (Rs is) small, the tip of the

stator flux S moves in the direction of stator voltage Vs ata speed proportional to the magnitude of Vs according to:

S = Vs Te (19)

The switching configuration is made step by step, inorder to maintain the stator flux and torque within limits

of two hysteresis bands. Where Te is the period in which

the voltage vector is applied to stator winding. Selectingstep by step the voltage vector appropriately, it is then

possible to drive s along a prefixed track curve [3].

V. SWITCHING STRATEGIES IN DTC FOR DTPIM

Since the projection of the output voltages generated bythe inverter in the plane (, ) are related to theelectromechanical energy conversion and the projection ofthe output voltages generated by the inverter in the plane(1, 2,), are related only to the electrical losses. Thus; thecontrol strategy allows us to use the maximum voltagevectors generated on the plane (, ) that maintain the

voltage vectors generated on the plane (1, 2) asminimum as possible.

For different phase shift angle () between the stator1

and stator2, the commutation modes generate the maximalamplitude voltage vectors are shown in the figures (6),(7), and (8).

A. The selected voltage vectors for= 30:

The projection of the 12 largest voltage vectorsgenerated by the inverter in (, ) are the 12 smallestvoltage vectors generated in (1, 2) for the sameswitching modes. So; the 12 vectors divide the plane (,) and (1, 2) in 12 sectors.

Fig.6. Projection of 12 selected vectors in (, ) and (1, 2)

corresponding to commutation modes for = 30.

B. The selected voltage vectors for= 0 and 60

The projection of the 6 largest voltage vectorsgenerated by the inverter in (, ), are the zero ones in (1,2) for the same switching modes. The largest non zero

vectors divide the plane (, ) into six sectors.

Fig.7. Projection of 6 selected vectors in (, ) and (u1, u2) correspondingto commutation modes for = 0.

Fig.8. Projection of 6 selected vectors in (, ) and (1, 2)corresponding to commutation modes for = 60.

Projection on the origin

0, 63, 7, 56, 41, 11, 26, 22, 52, 37


0, 63, 7, 56


0, 63, 7, 56, 9, 27, 18, 54, 36, 45Projection on the origin

0, 63, 7, 56


0, 63, 7, 56

axis axis 2

axis axis 1


0, 63, 7, 56

3011



6/8

V9 V11 V27 V26 V18 V22

s

em

V54 V52 V36 V37 V45 V41

s

em

VI. SWITCHING TABLE PROPOSED

A. Control technique of the flux and torque for= 0 and

60

Since the stator flux is created in the sector i = [1,...6],the vectors Vi+1 and Vi-1 are selected to increased the flux

amplitude while the vectors Vi+2 and Vi-2 are selected todecrease the amplitude of the stator flux. In the other side,the vectors Vi+1 and Vi+2 increase the torque while Vi-1 andVi-2 decrease the torque as it is shown in the Table.1 and

Table.2.

To improve the dynamic performance of DTC and toallow four-quadrant operation, it is necessary to involvethe voltage vectors VK-1 and VK-2 in torque and flux

control. Flux and torque control in this case are made by atwo-level hysteresis comparator.

For phase shift angle = 0:

TABLE. 2. Switching table for phase shift angle = 0.

Where ccpl and ccflx are respectively the ouputoftorque comparator and flux.

For phase shift angle = 60:

TABLE. 1. Switching table for phase shift angle = 60.

B. Control technique of the flux and torque for= 30:

For = 30 the projection of the 12 largest voltagevectors generated by the inverter in the plane (, ) are thesmallest 12 voltage vectors generated in the plane (1, 2)for the same switching modes. So; the 12 vectors divide

the plane (, ) and (1, 2) into 12 sectors.As The effect of the voltage vectors exists in the plane

(1, 2); it is necessary to use four non zero vectors (and

one null vector) per sampling period in order to controlboth planes simultaneously. As shown in fig.9, we alwaysselect the four vectors as being adjacent to the referencevector Vs while the corresponding vectors in (1, 2) are

approximately 180 out of phase, [7].The influence of the 12 largest vectors on the stator

flux and torque are illustrated in the table.3. The arrows

upward () or downward () represents the flux andtorque variation, which can be maximized or minimized ifthese voltage vectors are applied. Two arrows mean theinfluence on the flux or torque is medium and so on.

To design the switching table, the following, VK-1 andVK-2 denoted backward voltage vectors in

contraposition to forward voltage vectors utilised to

denote Vi+1 and Vi+2. A simple strategy which makes useof these voltage vectors is shown in fig.10.

Fig.9. Selection of the vectors for best control.

TABLE. 3. Stator flux and torque variation corresponding to selected

voltage vectors in the first sector

For flux control, let the variable E (E= s*- s) be

located in one of the three regions fixed by the contraints:

E < E min , E min E E max , E > E max .

The suitable flux level is then bounded by E min andEmax. Flux control is made by a two-level hysteresiscomparator. Three regions for flux location are noted, flux

as in fuzzy control schemes, by En (negative), Ez (zero)

and Ep (positive).

A high level performance torque control is required to

improve the torque control, let the difference (E = em*-

e) belong to one of the five regions defined by thecontraints :

E < Emin2 , Emin2 E Emin1 , Emin1 E Emax1 ,

Emax1 E Emax2 and Emax2 < E

The five regions defined for torque location are alsonoted , as in fuzzy control schemes, by Enl (negative

large), Ens (negative small), Ez (zero), Eps (positvesmall), Epl (positve large). The torque is then controlled by a hysteresis comparator built with two lower bounds

and two upper bounds, [8]. A switching table is used toselect the best output voltage depending on the position ofthe stator flux and desired action on the torque and statorflux. The flux position in the (, ) plane is quantified in

twelve sectors. The appropriate vector voltage is selectedin the order to reduce the number of commutation and the

level of steady state ripple.

Sectors s 1 2 3 4 5 6

ccpl1

ccflx 1 11 26 22 52 37 41

0 26 22 52 37 41 11

ccpl0

ccflx 1 37 41 11 26 22 52

0 52 37 41 11 26 22

Sectors s 1 2 3 4 5 6

ccpl1

ccflx 1 27 18 54 36 45 9

0 18 54 36 45 9 27

ccpl0

ccflx 1 45 9 27 18 54 36

0 36 45 9 27 18 54

3012



7/8

The switching strategy in the order of the sectors, isillustrated by each table. The flux and torque control byvector voltage has in nature a desecrate behavior.

In fact, we can easily verify that the same vector could

be adequate for a set of value ofs. The number of sectorsshould be as large as possible to have an adequate

decision, for this reason, we propose a new approach fordirect torque control using a six phase inverter based on

twelve regular sectors noted by 1 to 12.

Fig.10. Switching tables in DTC for DTPIM

VII. THE SIMULATION RESULTS

The validity of the proposed DTC algorithm for sixphase voltage source inverter is proved by the simulationresults. The used flux and torque contraints for the DTC

approach are expressed in percent with respect to the flux

and torque reference values :

E max = +3% , E min = -3% ,Emin2 = -3% ,Emin1 = -0.5% , Emax1 = +0.5% , Emax2 =+3%.

The simulation results illustrate both the steady stateand the transient performance of the proposed torquecontrol scheme for the three values of different phase shiftangle.

Fig.11, Fig.12, and Fig.13 show the phase current,stator flux, electromagnetic torque for steady state and

transient operation at 14 Nm with 1.2 Wb. The wave formof the stator current is closed to a sinusoidal signal, thetrajectory of the flux is nearly a circle and its amplitude

tracks the desired command value in very short timeresponse about 5ms. The output electromagnetic torquereaches the reference torque in about 3.5ms for phase shift

angle = 30, and 6 ms for = 0 and = 60.We note that, low flux ripple for = 30 compared to

that for = 0 and = 60. There is no harmonicsgenerated by the inverter in (1, 2) Subspace with ST-

DTC proposed for = 0 and = 60. But in the case of= 30, there is a distortion in the phase current wave formdue to the presence of harmonic components in (1, 2)Subspace, small voltage vectors are generated in this plane with the proposed strategy of commutation. For both methods the electromagnetic torque and stator fluxoscillate around their nominal values (14 N.m and 1.2

Wb) without notable overtaking but with an importantharmonic content.

Fig.14 shows that, fast torque response is obtained anda constant flux maintained during the torque reverseresponse from +14 N.m to -14 N.m and flux command at1.2 Wb. (without over current during the torquetransition).

Thus, the performance of DTC is proved, theelectromagnetic torque and stator flux are then controlledat their nominal values with optimal switching table.

Fig.11. Simulation results with rated values of the fluxand torque for phase shift =0.

P Z N

PL 27 18 54

PS 11 26 22

ZE 0 0 0

NS 9 45 36

NL 41 37 52

E

E

2

P Z N

PL 11 26 22

PS 9 27 18

ZE 0 0 0

NS 41 37 52

NL 45 36 54

E

E

1

P Z N

PL 18 54 36

PS 26 22 52

ZE 0 0 0

NS 27 9 45

NL 11 41 37

E

E

4

P Z N

PL 26 22 52

PS 27 18 54

ZE 0 0 0

NS 11 41 37

NL 9 45 36

E

E

3

P Z N

PL 54 36 45

PS 22 52 37

ZE 0 0 0

NS 18 27 9

NL 26 11 41

E

E

6

P Z N

PL 22 52 37

PS 18 54 36

ZE 0 0 0

NS 26 11 41

NL 27 9 45

E

E

5

P Z N

PL 36 45 9

PS 52 37 41

ZE 0 0 0

NS 54 18 27

NL 22 26 11

E

E

8

P Z N

PL 52 37 41

PS 54 36 45

ZE 0 0 0

NS 22 26 11

NL 18 27 9

E

E

7

P Z N

PL 45 9 27

PS 37 41 11

ZE 0 0 0

NS 36 54 18

NL 52 22 26

E

E

10

P Z N

PL 37 41 11

PS 36 45 9

ZE 0 0 0

NS 52 22 26

NL 54 18 27

E

E

9

P Z N

PL 9 27 18

PS 41 11 26

ZE 0 0 0

NS 45 36 54

NL 37 52 22

E

E

12

P Z N

PL 41 11 26

PS 45 9 27

ZE 0 0 0

NS 37 52 22

NL 36 54 18

E

E

11

Torque(N.m

)

s

(s

)

Statorflux(wb)

Phasecurrent(A)

Time (s)Time (s)

Time (s)

3013



8/8

Fig.12. Simulation results with rated values of the flux

and torque for phase shift =30.

Fig.13. Simulation results with rated values of the flux

and torque for phase shift = 60.

Fig.14. Stator current in the phase a s1 and electric torque reverse

response of the motor

VIII. CONCLUSIONS

The multi-phase machine drives is very interesting forhigh power and high current application. Since the sixthharmonic torque pulsations were predominant and mainlyproduced due to the interaction between the fundamentalflux and the fifth and seventh harmonic rotor currents andin order to eliminate the sixth harmonic torque pulsations,

dual three-phase induction machine is used. In thisconfiguration, the sixth harmonic torque pulsations produced by the two sets of windings are in opposite phase. So, the sixth harmonic torque pulsations arecompletely absent in DTPIM. Therefore, today the sixth

harmonic torque pulsations are not an issue, [9].

The complexity of the analysis has been solved byusing matrix theory and the concept of the vector spacedecomposition (VSD). This theory was introduced totransform the original six-dimensional space of themachine into three two dimensional orthogonal subspaces by using a proper 6x6 transformation matrix. Then, the

modeling and the control is greatly simplified in the newreference frame.

The analytical modeling and the control of the DTPIM

is accomplished in three two dimensional orthogonalsubspaces, such that the dynamics of theelectromechanically energy conversion and the non-electromechanically energy conversion related to the

machine variables are totally decoupled.The feasibility of DTC control of DTPIM has been

validated by simulation and the results obtained shows

that the direct torque control method gives fast and gooddynamic response. The effect of the shift angle betweenthe two three-phase windings on the dynamicperformances and the DTC strategy are carried out.In this paper, DTC system using six-phase fed dual-threephase induction motor is presented, it is suitable for high-power and high-current applications.

REFERENCES

[1] Yifan Zhao and Thomas A. Lipo, Space Vector PWM Control of

Dual Three-Phase Induction Machine Using Vector SpaceDecomposition., IEEE, Trans. Ind. App, vol.31, No.05,

Sept/Oct.1995, pp.1100-1109.

[2] Lin. Chen and Fan. Yang, Unified Voltage Modulation for Dual-Three-Phase Induction Motor, Proceeding of the Third

International Cconference on Machine Learning and Cybernetics,

Shanghai, 26-29 August 2004 IEEE, pp.672-677.[3] I. Takahashi and T. Noguchi, A New Quick-Response and High-

Efficiency Control Strategy of an Induction Motor. IEEE Trans.

on IA, vol. 22, No. 5, Sept/Oct. 1986, pp. 820-827.[4] WU. Xuezh, and L. Huang, Direct Torque Control of Three-

Level Inverter Using Neural Networks as Switching Vector

Selector. IEEE IAS, annual meeting, 30 Sept\ 04 Oct.2001.[5] Radu Dojoi, Alberto Tenconi, and Francessco Profumo, A Vector

Control of Dual-Three-Phase Induction Motor Drives Using TwoCurrent Sensor, IEEE, Trans. Ind. App, vol.42, No.05,

Sept/Oct.2006. pp.1284-1292.[6] D. Casadei, G. Grandi, G. Serra, and A. Tani, Switching strategies

in direct torque control of induction machines. ICEM 94, vol. 2,

1994, pp.204-209.

[7] D. Hadiouche, Contribution ltude de la machine Asynchronea Double toile: Modlisation, Alimentation, et Structure, Thse

de Doctorat, Ecole Doctorale, Informatique, Automatique,

Electrotechnique, Electronique, Mathmatique. Universit deHENRI POINKARE, 20 Dcembre 2001.

[8] R. Zaimeddine, E.M. Berkouk, L. Refoufi; A Scheme of EDTC

Control Using an Induction Motor Three-Level Voltage SourceInverter for Electric Vehicles, Journal of Electrical Engineering

and Technology (JEET), Publication of the Korean Institute of

Electrical Engineers, Vol.2, No. 4, Dec 2007, PP 505-512.[9] Kmalesh Hatua, and V.T.Ranganathan, Direct Torque Control

Schemes of Split-Phase Induction Machines, IEEE, Trans. Ind.

Applicat, vol.41, No.05, September/October.2005. , pp.1243-1254.

Time (s)

Time (s)Time (s)

s

(s

)

Torque(N.m

)

Statorflux(wb)

Phasecurrent(A)

Time (s)

Statorflux(wb)

Torque(N.m

)

Phasecurrent(A)

s

(s

)

Time (s)Time (s)

Time (s)Time (s)

Torque(N.m

)

Phasecurrent(A)

3014


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